Interpolating data¶
Xarray offers flexible interpolation routines, which have a similar interface to our indexing.
Note
interp
requires scipy installed.
Scalar and 1-dimensional interpolation¶
Interpolating a DataArray
works mostly like labeled
indexing of a DataArray
,
In [1]: da = xr.DataArray(
...: np.sin(0.3 * np.arange(12).reshape(4, 3)),
...: [("time", np.arange(4)), ("space", [0.1, 0.2, 0.3])],
...: )
...:
# label lookup
In [2]: da.sel(time=3)
Out[2]:
<xarray.DataArray (space: 3)>
array([ 0.427, 0.141, -0.158])
Coordinates:
time int64 3
* space (space) float64 0.1 0.2 0.3
# interpolation
In [3]: da.interp(time=2.5)
Out[3]:
<xarray.DataArray (space: 3)>
array([0.701, 0.502, 0.259])
Coordinates:
* space (space) float64 0.1 0.2 0.3
time float64 2.5
Similar to the indexing, interp()
also accepts an
array-like, which gives the interpolated result as an array.
# label lookup
In [4]: da.sel(time=[2, 3])
Out[4]:
<xarray.DataArray (time: 2, space: 3)>
array([[ 0.974, 0.863, 0.675],
[ 0.427, 0.141, -0.158]])
Coordinates:
* time (time) int64 2 3
* space (space) float64 0.1 0.2 0.3
# interpolation
In [5]: da.interp(time=[2.5, 3.5])
Out[5]:
<xarray.DataArray (time: 2, space: 3)>
array([[0.701, 0.502, 0.259],
[ nan, nan, nan]])
Coordinates:
* space (space) float64 0.1 0.2 0.3
* time (time) float64 2.5 3.5
To interpolate data with a numpy.datetime64 coordinate you can pass a string.
In [6]: da_dt64 = xr.DataArray(
...: [1, 3], [("time", pd.date_range("1/1/2000", "1/3/2000", periods=2))]
...: )
...:
In [7]: da_dt64.interp(time="2000-01-02")
Out[7]:
<xarray.DataArray ()>
array(2.)
Coordinates:
time datetime64[ns] 2000-01-02
The interpolated data can be merged into the original DataArray
by specifying the time periods required.
In [8]: da_dt64.interp(time=pd.date_range("1/1/2000", "1/3/2000", periods=3))
Out[8]:
<xarray.DataArray (time: 3)>
array([1., 2., 3.])
Coordinates:
* time (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03
Interpolation of data indexed by a CFTimeIndex
is also
allowed. See Non-standard calendars and dates outside the nanosecond-precision range for examples.
Note
Currently, our interpolation only works for regular grids.
Therefore, similarly to sel()
,
only 1D coordinates along a dimension can be used as the
original coordinate to be interpolated.
Multi-dimensional Interpolation¶
Like sel()
, interp()
accepts multiple coordinates. In this case, multidimensional interpolation
is carried out.
# label lookup
In [9]: da.sel(time=2, space=0.1)
Out[9]:
<xarray.DataArray ()>
array(0.974)
Coordinates:
time int64 2
space float64 0.1
# interpolation
In [10]: da.interp(time=2.5, space=0.15)
Out[10]:
<xarray.DataArray ()>
array(0.601)
Coordinates:
time float64 2.5
space float64 0.15
Array-like coordinates are also accepted:
# label lookup
In [11]: da.sel(time=[2, 3], space=[0.1, 0.2])
Out[11]:
<xarray.DataArray (time: 2, space: 2)>
array([[0.974, 0.863],
[0.427, 0.141]])
Coordinates:
* time (time) int64 2 3
* space (space) float64 0.1 0.2
# interpolation
In [12]: da.interp(time=[1.5, 2.5], space=[0.15, 0.25])
Out[12]:
<xarray.DataArray (time: 2, space: 2)>
array([[0.888, 0.867],
[0.601, 0.381]])
Coordinates:
* time (time) float64 1.5 2.5
* space (space) float64 0.15 0.25
interp_like()
method is a useful shortcut. This
method interpolates an xarray object onto the coordinates of another xarray
object. For example, if we want to compute the difference between
two DataArray
s (da
and other
) staying on slightly
different coordinates,
In [13]: other = xr.DataArray(
....: np.sin(0.4 * np.arange(9).reshape(3, 3)),
....: [("time", [0.9, 1.9, 2.9]), ("space", [0.15, 0.25, 0.35])],
....: )
....:
it might be a good idea to first interpolate da
so that it will stay on the
same coordinates of other
, and then subtract it.
interp_like()
can be used for such a case,
# interpolate da along other's coordinates
In [14]: interpolated = da.interp_like(other)
In [15]: interpolated
Out[15]:
<xarray.DataArray (time: 3, space: 3)>
array([[0.787, 0.911, nan],
[0.912, 0.789, nan],
[0.348, 0.069, nan]])
Coordinates:
* time (time) float64 0.9 1.9 2.9
* space (space) float64 0.15 0.25 0.35
It is now possible to safely compute the difference other - interpolated
.
Interpolation methods¶
We use scipy.interpolate.interp1d
for 1-dimensional interpolation.
For multi-dimensional interpolation, an attempt is first made to decompose the
interpolation in a series of 1-dimensional interpolations, in which case
scipy.interpolate.interp1d
is used. If a decomposition cannot be
made (e.g. with advanced interpolation), scipy.interpolate.interpn()
is
used.
The interpolation method can be specified by the optional method
argument.
In [16]: da = xr.DataArray(
....: np.sin(np.linspace(0, 2 * np.pi, 10)),
....: dims="x",
....: coords={"x": np.linspace(0, 1, 10)},
....: )
....:
In [17]: da.plot.line("o", label="original")
Out[17]: [<matplotlib.lines.Line2D at 0x7f855892e4d0>]
In [18]: da.interp(x=np.linspace(0, 1, 100)).plot.line(label="linear (default)")
Out[18]: [<matplotlib.lines.Line2D at 0x7f855636f6d0>]
In [19]: da.interp(x=np.linspace(0, 1, 100), method="cubic").plot.line(label="cubic")
Out[19]: [<matplotlib.lines.Line2D at 0x7f8557d90090>]
In [20]: plt.legend()
Out[20]: <matplotlib.legend.Legend at 0x7f85562d5f50>

Additional keyword arguments can be passed to scipy’s functions.
# fill 0 for the outside of the original coordinates.
In [21]: da.interp(x=np.linspace(-0.5, 1.5, 10), kwargs={"fill_value": 0.0})
Out[21]:
<xarray.DataArray (x: 10)>
array([ 0. , 0. , 0. , 0.814, 0.604, -0.604, -0.814, 0. , 0. , 0. ])
Coordinates:
* x (x) float64 -0.5 -0.2778 -0.05556 0.1667 ... 0.8333 1.056 1.278 1.5
# 1-dimensional extrapolation
In [22]: da.interp(x=np.linspace(-0.5, 1.5, 10), kwargs={"fill_value": "extrapolate"})
Out[22]:
<xarray.DataArray (x: 10)>
array([-2.893, -1.607, -0.321, 0.814, 0.604, -0.604, -0.814, 0.321, 1.607, 2.893])
Coordinates:
* x (x) float64 -0.5 -0.2778 -0.05556 0.1667 ... 0.8333 1.056 1.278 1.5
# multi-dimensional extrapolation
In [23]: da = xr.DataArray(
....: np.sin(0.3 * np.arange(12).reshape(4, 3)),
....: [("time", np.arange(4)), ("space", [0.1, 0.2, 0.3])],
....: )
....:
In [24]: da.interp(
....: time=4, space=np.linspace(-0.1, 0.5, 10), kwargs={"fill_value": "extrapolate"}
....: )
....:
Out[24]:
<xarray.DataArray (space: 10)>
array([ 0.805, 0.497, 0.189, -0.119, -0.427, -0.718, -0.991, -1.264, -1.538, -1.811])
Coordinates:
time int64 4
* space (space) float64 -0.1 -0.03333 0.03333 0.1 ... 0.3 0.3667 0.4333 0.5
Advanced Interpolation¶
interp()
accepts DataArray
as similar to sel()
, which enables us more advanced interpolation.
Based on the dimension of the new coordinate passed to interp()
, the dimension of the result are determined.
For example, if you want to interpolate a two dimensional array along a particular dimension, as illustrated below,
you can pass two 1-dimensional DataArray
s with
a common dimension as new coordinate.
For example:
In [25]: da = xr.DataArray(
....: np.sin(0.3 * np.arange(20).reshape(5, 4)),
....: [("x", np.arange(5)), ("y", [0.1, 0.2, 0.3, 0.4])],
....: )
....:
# advanced indexing
In [26]: x = xr.DataArray([0, 2, 4], dims="z")
In [27]: y = xr.DataArray([0.1, 0.2, 0.3], dims="z")
In [28]: da.sel(x=x, y=y)
Out[28]:
<xarray.DataArray (z: 3)>
array([ 0. , 0.427, -0.773])
Coordinates:
x (z) int64 0 2 4
y (z) float64 0.1 0.2 0.3
Dimensions without coordinates: z
# advanced interpolation, without extrapolation
In [29]: x = xr.DataArray([0.5, 1.5, 2.5, 3.5], dims="z")
In [30]: y = xr.DataArray([0.15, 0.25, 0.35, 0.45], dims="z")
In [31]: da.interp(x=x, y=y)
Out[31]:
<xarray.DataArray (z: 4)>
array([ 0.556, 0.635, -0.466, nan])
Coordinates:
x (z) float64 0.5 1.5 2.5 3.5
y (z) float64 0.15 0.25 0.35 0.45
Dimensions without coordinates: z
where values on the original coordinates
(x, y) = ((0.5, 0.15), (1.5, 0.25), (2.5, 0.35), (3.5, 0.45))
are obtained
by the 2-dimensional interpolation and mapped along a new dimension z
. Since
no keyword arguments are passed to the interpolation routine, no extrapolation
is performed resulting in a nan
value.
If you want to add a coordinate to the new dimension z
, you can supply
DataArray
s with a coordinate. Extrapolation can be achieved
by passing additional arguments to SciPy’s interpnd
function,
In [32]: x = xr.DataArray([0.5, 1.5, 2.5, 3.5], dims="z", coords={"z": ["a", "b", "c", "d"]})
In [33]: y = xr.DataArray(
....: [0.15, 0.25, 0.35, 0.45], dims="z", coords={"z": ["a", "b", "c", "d"]}
....: )
....:
In [34]: da.interp(x=x, y=y, kwargs={"fill_value": None})
Out[34]:
<xarray.DataArray (z: 4)>
array([ 0.556, 0.635, -0.466, -0.735])
Coordinates:
x (z) float64 0.5 1.5 2.5 3.5
y (z) float64 0.15 0.25 0.35 0.45
* z (z) <U1 'a' 'b' 'c' 'd'
For the details of the advanced indexing, see more advanced indexing.
Interpolating arrays with NaN¶
Our interp()
works with arrays with NaN
the same way that
scipy.interpolate.interp1d and
scipy.interpolate.interpn do.
linear
and nearest
methods return arrays including NaN,
while other methods such as cubic
or quadratic
return all NaN arrays.
In [35]: da = xr.DataArray([0, 2, np.nan, 3, 3.25], dims="x", coords={"x": range(5)})
In [36]: da.interp(x=[0.5, 1.5, 2.5])
Out[36]:
<xarray.DataArray (x: 3)>
array([ 1., nan, nan])
Coordinates:
* x (x) float64 0.5 1.5 2.5
In [37]: da.interp(x=[0.5, 1.5, 2.5], method="cubic")
Out[37]:
<xarray.DataArray (x: 3)>
array([nan, nan, nan])
Coordinates:
* x (x) float64 0.5 1.5 2.5
To avoid this, you can drop NaN by dropna()
, and
then make the interpolation
In [38]: dropped = da.dropna("x")
In [39]: dropped
Out[39]:
<xarray.DataArray (x: 4)>
array([0. , 2. , 3. , 3.25])
Coordinates:
* x (x) int64 0 1 3 4
In [40]: dropped.interp(x=[0.5, 1.5, 2.5], method="cubic")
Out[40]:
<xarray.DataArray (x: 3)>
array([1.19 , 2.508, 2.93 ])
Coordinates:
* x (x) float64 0.5 1.5 2.5
If NaNs are distributed randomly in your multidimensional array,
dropping all the columns containing more than one NaNs by
dropna()
may lose a significant amount of information.
In such a case, you can fill NaN by interpolate_na()
,
which is similar to pandas.Series.interpolate()
.
In [41]: filled = da.interpolate_na(dim="x")
In [42]: filled
Out[42]:
<xarray.DataArray (x: 5)>
array([0. , 2. , 2.5 , 3. , 3.25])
Coordinates:
* x (x) int64 0 1 2 3 4
This fills NaN by interpolating along the specified dimension. After filling NaNs, you can interpolate:
In [43]: filled.interp(x=[0.5, 1.5, 2.5], method="cubic")
Out[43]:
<xarray.DataArray (x: 3)>
array([1.309, 2.316, 2.738])
Coordinates:
* x (x) float64 0.5 1.5 2.5
For the details of interpolate_na()
,
see Missing values.
Example¶
Let’s see how interp()
works on real data.
# Raw data
In [44]: ds = xr.tutorial.open_dataset("air_temperature").isel(time=0)
---------------------------------------------------------------------------
ModuleNotFoundError Traceback (most recent call last)
File /build/python-xarray-AyGMZw/python-xarray-2023.05.0/xarray/tutorial.py:126, in open_dataset(name, cache, cache_dir, engine, **kws)
125 try:
--> 126 import pooch
127 except ImportError as e:
ModuleNotFoundError: No module named 'pooch'
The above exception was the direct cause of the following exception:
ImportError Traceback (most recent call last)
Cell In [44], line 1
----> 1 ds = xr.tutorial.open_dataset("air_temperature").isel(time=0)
File /build/python-xarray-AyGMZw/python-xarray-2023.05.0/xarray/tutorial.py:128, in open_dataset(name, cache, cache_dir, engine, **kws)
126 import pooch
127 except ImportError as e:
--> 128 raise ImportError(
129 "tutorial.open_dataset depends on pooch to download and manage datasets."
130 " To proceed please install pooch."
131 ) from e
133 logger = pooch.get_logger()
134 logger.setLevel("WARNING")
ImportError: tutorial.open_dataset depends on pooch to download and manage datasets. To proceed please install pooch.
In [45]: fig, axes = plt.subplots(ncols=2, figsize=(10, 4))
In [46]: ds.air.plot(ax=axes[0])
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Cell In [46], line 1
----> 1 ds.air.plot(ax=axes[0])
File /build/python-xarray-AyGMZw/python-xarray-2023.05.0/xarray/core/common.py:278, in AttrAccessMixin.__getattr__(self, name)
276 with suppress(KeyError):
277 return source[name]
--> 278 raise AttributeError(
279 f"{type(self).__name__!r} object has no attribute {name!r}"
280 )
AttributeError: 'Dataset' object has no attribute 'air'
In [47]: axes[0].set_title("Raw data")
Out[47]: Text(0.5, 1.0, 'Raw data')
# Interpolated data
In [48]: new_lon = np.linspace(ds.lon[0], ds.lon[-1], ds.dims["lon"] * 4)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Cell In [48], line 1
----> 1 new_lon = np.linspace(ds.lon[0], ds.lon[-1], ds.dims["lon"] * 4)
File /build/python-xarray-AyGMZw/python-xarray-2023.05.0/xarray/core/common.py:278, in AttrAccessMixin.__getattr__(self, name)
276 with suppress(KeyError):
277 return source[name]
--> 278 raise AttributeError(
279 f"{type(self).__name__!r} object has no attribute {name!r}"
280 )
AttributeError: 'Dataset' object has no attribute 'lon'
In [49]: new_lat = np.linspace(ds.lat[0], ds.lat[-1], ds.dims["lat"] * 4)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Cell In [49], line 1
----> 1 new_lat = np.linspace(ds.lat[0], ds.lat[-1], ds.dims["lat"] * 4)
File /build/python-xarray-AyGMZw/python-xarray-2023.05.0/xarray/core/common.py:278, in AttrAccessMixin.__getattr__(self, name)
276 with suppress(KeyError):
277 return source[name]
--> 278 raise AttributeError(
279 f"{type(self).__name__!r} object has no attribute {name!r}"
280 )
AttributeError: 'Dataset' object has no attribute 'lat'
In [50]: dsi = ds.interp(lat=new_lat, lon=new_lon)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [50], line 1
----> 1 dsi = ds.interp(lat=new_lat, lon=new_lon)
NameError: name 'new_lat' is not defined
In [51]: dsi.air.plot(ax=axes[1])
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [51], line 1
----> 1 dsi.air.plot(ax=axes[1])
NameError: name 'dsi' is not defined
In [52]: axes[1].set_title("Interpolated data")
Out[52]: Text(0.5, 1.0, 'Interpolated data')

Our advanced interpolation can be used to remap the data to the new coordinate. Consider the new coordinates x and z on the two dimensional plane. The remapping can be done as follows
# new coordinate
In [53]: x = np.linspace(240, 300, 100)
In [54]: z = np.linspace(20, 70, 100)
# relation between new and original coordinates
In [55]: lat = xr.DataArray(z, dims=["z"], coords={"z": z})
In [56]: lon = xr.DataArray(
....: (x[:, np.newaxis] - 270) / np.cos(z * np.pi / 180) + 270,
....: dims=["x", "z"],
....: coords={"x": x, "z": z},
....: )
....:
In [57]: fig, axes = plt.subplots(ncols=2, figsize=(10, 4))
In [58]: ds.air.plot(ax=axes[0])
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Cell In [58], line 1
----> 1 ds.air.plot(ax=axes[0])
File /build/python-xarray-AyGMZw/python-xarray-2023.05.0/xarray/core/common.py:278, in AttrAccessMixin.__getattr__(self, name)
276 with suppress(KeyError):
277 return source[name]
--> 278 raise AttributeError(
279 f"{type(self).__name__!r} object has no attribute {name!r}"
280 )
AttributeError: 'Dataset' object has no attribute 'air'
# draw the new coordinate on the original coordinates.
In [59]: for idx in [0, 33, 66, 99]:
....: axes[0].plot(lon.isel(x=idx), lat, "--k")
....:
In [60]: for idx in [0, 33, 66, 99]:
....: axes[0].plot(*xr.broadcast(lon.isel(z=idx), lat.isel(z=idx)), "--k")
....:
In [61]: axes[0].set_title("Raw data")
Out[61]: Text(0.5, 1.0, 'Raw data')
In [62]: dsi = ds.interp(lon=lon, lat=lat)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Cell In [62], line 1
----> 1 dsi = ds.interp(lon=lon, lat=lat)
File /build/python-xarray-AyGMZw/python-xarray-2023.05.0/xarray/core/dataset.py:3382, in Dataset.interp(self, coords, method, assume_sorted, kwargs, method_non_numeric, **coords_kwargs)
3379 kwargs = {}
3381 coords = either_dict_or_kwargs(coords, coords_kwargs, "interp")
-> 3382 indexers = dict(self._validate_interp_indexers(coords))
3384 if coords:
3385 # This avoids broadcasting over coordinates that are both in
3386 # the original array AND in the indexing array. It essentially
3387 # forces interpolation along the shared coordinates.
3388 sdims = (
3389 set(self.dims)
3390 .intersection(*[set(nx.dims) for nx in indexers.values()])
3391 .difference(coords.keys())
3392 )
File /build/python-xarray-AyGMZw/python-xarray-2023.05.0/xarray/core/dataset.py:2385, in Dataset._validate_interp_indexers(self, indexers)
2381 def _validate_interp_indexers(
2382 self, indexers: Mapping[Any, Any]
2383 ) -> Iterator[tuple[Hashable, Variable]]:
2384 """Variant of _validate_indexers to be used for interpolation"""
-> 2385 for k, v in self._validate_indexers(indexers):
2386 if isinstance(v, Variable):
2387 if v.ndim == 1:
File /build/python-xarray-AyGMZw/python-xarray-2023.05.0/xarray/core/dataset.py:2349, in Dataset._validate_indexers(self, indexers, missing_dims)
2346 from xarray.coding.cftimeindex import CFTimeIndex
2347 from xarray.core.dataarray import DataArray
-> 2349 indexers = drop_dims_from_indexers(indexers, self.dims, missing_dims)
2351 # all indexers should be int, slice, np.ndarrays, or Variable
2352 for k, v in indexers.items():
File /build/python-xarray-AyGMZw/python-xarray-2023.05.0/xarray/core/utils.py:859, in drop_dims_from_indexers(indexers, dims, missing_dims)
857 invalid = indexers.keys() - set(dims)
858 if invalid:
--> 859 raise ValueError(
860 f"Dimensions {invalid} do not exist. Expected one or more of {dims}"
861 )
863 return indexers
865 elif missing_dims == "warn":
866 # don't modify input
ValueError: Dimensions {'lat', 'lon'} do not exist. Expected one or more of Frozen({'x': 3, 'y': 4})
In [63]: dsi.air.plot(ax=axes[1])
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [63], line 1
----> 1 dsi.air.plot(ax=axes[1])
NameError: name 'dsi' is not defined
In [64]: axes[1].set_title("Remapped data")
Out[64]: Text(0.5, 1.0, 'Remapped data')
